1. Field of the invention
The present invention relates to a field effect transistor (FET) having quantum-wave interference layers that reflect carriers, or electrons and holes, effectively. In particular, the invention relates to field effect transistors including a metal semiconductor field effect transistor (MESFET) having a Schottky junction structure, a metal oxide semiconductor field effect transistor (MOSFET), and a high electron mobility transistor (HEMT) in which carriers are effectively confined in a channel region and used effectively by reflecting the carriers to prevent them from leaking to other region.
2. Description of the Related Art
Plural MOSFETs on a large-scale integrated (LSI) circuit have been known little to have a method to avoid leakage current from a source (S) into the drains (Dxe2x80x2) of other transistor. Because voltage is applied to gate regions sandwiching a channel (C) region, impurities are doped to the lower gate region of a semiconductor which is used to form a MOSFET. As a result, the method to avoid leakage current is considered to be difficult.
As a countermeasure, reflecting carriers by forming cladding layers with a multi-quantum well structure of a first and a second layers as a unit in a laser diode (LD) has been suggested by Takagi et al. (Japanese Journal of Applied Physics. Vol.29, No.11, November 1990, pp.L1977-L1980). Although it can be led that a band gap energy is used as an alternative of a kinetic energy, this reference does not teach or suggest values of kinetic energy of carriers to be considered and the degree of luminous intensity improvement is inadequate.
The inventor of the present invention conducted a series of experiments and found that the suggested thicknesses of the first and the second layers by Takagi et al. were too small to reflect carriers, and that preferable thicknesses of the first and second layers are 4 to 6 times larger than those suggested by Takagi et al. Further, the present inventors thought that multiple reflection of quantum-waves of carriers might occur by a multi-layer structure with different band width, like multiple reflection of light by a dielectic multi-film structure. And the inventors thought that it would be possible to increase threshold of the external voltage at which a current starts to flow by the quantum-wave reflection. As a result, the inventors invented a preferable quantum-wave interference layer and applications of the same.
It is, therefore, an object of the present invention to provide a field effect transistor having a novel junction structure with considerably larger threshold of voltage at which a current starts to flow by forming a quantum-wave interference layer in a lower gate region adjacent to a channel.
In light of these objects a first aspect of the present invention is a field effect transistor comprising a quantum-wave interference layer having plural periods of a pair of a first layer and a second layer in a region adjacent to a channel, the second layer having a wider band gap than the first layer. Each thickness of the first and the second layers is determined by multiplying by an odd number one fourth of quantum-wave wavelength of carriers in each of the first and the second layers, which exist around the lowest energy level of the second layer.
The second aspect of the present invention is a field effect transistor comprising a quantum-wave interference layer having plural periods of a pair of a first layer and a second layer as a unit in a region adjacent to a channel. The second layer has a wider band gap than the first layer. A xcex4 layer is included for sharply varying energy band and is formed between the first and the second layers. Each thickness of the first and the second layers is determined by multiplying by an odd number one fourth of quantum-wave wavelength of carriers in each of the first and the second layers, and a thickness of the xcex4 layer is substantially thinner than that of the first and the second layers.
The third aspect of the present invention is to define each thickness of the first and the second layers as follows:
DW=nWxcexW/4=nWh/4[2mW(E+V)]xc2xdxe2x80x83xe2x80x83(1)
and
DB=nBxcexB/4=nBh/4(2mBE)xc2xdxe2x80x83xe2x80x83(2)
In Eqs. 1 and 2, h, mW, mB, E, V, and nW, nB represent a Plank""s constant, effective mass of carriers in the first layer, effective mass of carriers in the second layer, kinetic energy of carriers at the lowest energy level around the second layer, potential energy of the second layer to the first layer, and odd numbers, respectively.
The fourth aspect of the present invention is a field effect transistor having a plurality of partial quantum-wave interference layers Ik with arbitrary periods Tk including a first layer having a thickness of DWk and a second layer having a thickness of DBk and arranged in series. The thicknesses of the first and the second layers satisfy the formulas:
DWk=nWkxcexWk/4=nWkh/4[2mWk(Ek+V)]xc2xdxe2x80x83xe2x80x83(3)
and
DBk=nBkxcexBk/4=nBkh/4(2mBkEk)xc2xdxe2x80x83xe2x80x83(4)
In Eqs. 3 and 4, Ek, mWk, mBk, and nWk and nBk represent plural kinetic energy levels of carriers flowing into the second layer, effective mass of minority carriers with kinetic energy Ek+V in the first layer, effective mass of carriers with kinetic energy Ek in the second layer, and arbitrary odd numbers, respectively.
The plurality of the partial quantum-wave interference layers Ik are arranged in series from I1 to Ij, where j is a maximum number of k required to form a quantum-wave interference layer as a whole.
The fifth aspect of the present invention is a transistor having a quantum-wave interference layer with a plurality of partial quantum-wave interference layers arranged in series with arbitrary periods. Each of the plurality of partial quantum-wave interference layers is constructed with serial pairs of the first and second layers. The widths of the first and second layers of the serial pairs are represented by (DW1, DB1), . . . , (DWk, DBk), (DWj, DBj). (DWk, DBk) is a pair of widths of the first and second layers and is defined as Eqs. 3 and 4, respectively.
The sixth aspect of the present invention is to form a xcex4 layer between a first layer and a second layer which sharply varies the energy band and has a thickness substantially thinner than that of the first and the second layers.
The seventh aspect of the present invention is to use the quantum-wave interference layer as a reflecting layer for reflecting carriers.
The eighth aspect of the present invention is to constitute a quantum-wave incident facet in the quantum-wave interference layer by a second layer with enough thickness for preventing conduction of carriers by a tunneling effect.
The principle of the quantum-wave interference layer of the present invention is explained hereinafter. The quantum-wave interference layer is formed in, i.e., a p-layer, which is formed beneath an inversion layer of a field effect transistor. FIG. 1 shows a conduction band of a quantum-wave interference layer with plural periods of a first layer W and a second layer B as a unit. A band gap of the second layer B is wider than that of a first layer. In a channel, electrons as minority carriers flow from a source to a drain. Electrons which leak to the p-layer formed beneath the channel, conduct from left to right as shown by an arrow in FIG. 1. Among the electrons, those that existing around the bottom of the second layer B are likely to contribute to conduction. The electrons around the bottom of the second layer B has a kinetic energy E. Accordingly, the electrons in the first layer W have a kinetic energy E+V which is accelerated by potential energy V due to the band gap between the first layer W and the second layer B. In other words, electrons that move from the first layer W to the second layer B are decelerated by potential energy V and return to the original kinetic energy E in the second layer B. As explained above, kinetic energy of electrons in the conduction band is modulated by potential energy due to the multi-layer structure of the quantum-wave interference layer.
When thickness of the first layer W and the second layer B are equal to order of a quantum-wave wavelength, electrons tend to have characteristics of a wave. The wave length of the electron quantum-wave is calculated by Eqs. 1 and 2 using kinetic energy of the electron. Further, defining the respective wave number vector in first layer W and second layer B as KW and KB, reflectivity R of the wave is calculated by:                                                         R              =                              xe2x80x83                            ⁢                                                (                                                            "LeftBracketingBar"                                              K                        W                                            "RightBracketingBar"                                        -                                          "LeftBracketingBar"                                              K                        B                                            "RightBracketingBar"                                                        )                                /                                  (                                                            "LeftBracketingBar"                                              K                        W                                            "RightBracketingBar"                                        +                                          "LeftBracketingBar"                                              K                        B                                            "RightBracketingBar"                                                        )                                                                                                        =                              xe2x80x83                            ⁢                                                [                                                                                    {                                                                              m                            W                                                    ⁡                                                      (                                                          E                              +                              V                                                        )                                                                          }                                                                    1                        /                        2                                                              -                                                                  (                                                                              m                            B                                                    ⁢                          E                                                )                                                                    1                        /                        2                                                                              ]                                /                                  [                                                                                    {                                                                              m                            W                                                    ⁡                                                      (                                                          E                              +                              V                                                        )                                                                          }                                                                    1                        /                        2                                                              +                                                                  (                                                                              m                            B                                                    ⁢                          E                                                )                                                                    1                        /                        2                                                                              ]                                                                                                        =                              xe2x80x83                            ⁢                                                [                                      1                    -                                                                  {                                                                              m                            B                                                    ⁢                                                      E                            /                                                                                          m                                W                                                            ⁡                                                              (                                                                  E                                  +                                  V                                                                )                                                                                                                                    }                                                                    1                        /                        2                                                                              ]                                /                                  [                                      1                    +                                                                  {                                                                              m                            B                                                    ⁢                                                      E                            /                                                                                          m                                W                                                            ⁡                                                              (                                                                  E                                  +                                  V                                                                )                                                                                                                                    }                                                                    1                        /                        2                                                                              ]                                                                                        (        5        )            
Further, when mB=mW, the reflectivity R is calculated by:
R=[1xe2x88x92{E/(E+V)}1/2]/[1+{E/(E+V)}1/2]xe2x80x83xe2x80x83(6).
When E/(E+V)=x, Eq. 6 is transformed into:
R=(1xe2x88x92xxc2xd)/(1+xxc2xd)xe2x80x83xe2x80x83(7).
The characteristic of the reflectivity R with respect to energy ratio x obtained by Eq. 7 is shown in FIG. 2.
When the second layer B and the first layer W have S periods, the reflectivity RS on the incident facet of a quantum-wave is calculated by:
RS=[(1xe2x88x92xS)/(1+xS)]2xe2x80x83xe2x80x83(8).
When the formula xxe2x89xa6{fraction (1/10)} is satisfied, Rxe2x89xa70.52. Accordingly, the relation between E and V is satisfied with:
Exe2x89xa6V/9xe2x80x83xe2x80x83(9)
Since the kinetic energy E of conducting electrons in the second layer B exists around the bottom of the conduction band, the relation of Eq. 9 is satisfied and the reflectivity R at the interface between the second layer B and the first layer W becomes 52% or more. Consequently, the multi-quantum well structure having two kinds of layers with different band gaps to each other enables to reflect quantum-wave of the electrons injected into the p-layer effectively.
Further, utilizing the energy ratio x enables thickness ratio DB/DW of the second layer B to the first layer W to be obtained by:
DB/DW=[mW/(mBx)]xc2xdxe2x80x83xe2x80x83(10).
The kinetic energy of electrons flowing in a channel from a source to a drain does not exceed-the-level used to design a thickness of a quantum-wave interference layer in the p-layer formed beneath a channel in a field effect transistor substantially. As a result, electrons are reflected and do not cause leakage current to the p-layer formed beneath a channel.
Thicknesses of the first layer W and the second layer B are determined for selectively reflecting either one of holes and electrons, because of a difference in potential energy between the valence and the conduction bands, and a difference in effective mass of holes and electrons in the first layer W and the second layer B. Namely, the optimum thickness for reflecting electrons is not optimum for reflecting holes. Eqs. 5-10 refer to a structure of the quantum-wave interference layer for reflecting electrons selectively. The thickness for selectively reflecting electrons is designed based on a difference in potential energy of the conduction band and effective mass of electrons.
Further, the thickness for selectively reflecting holes is designed based on a difference in potential energy of the valence band and effective mass of holes, realizing another type of quantum-wave interference layer, formed in a field effect transistor having a channel region as an n-layer, for reflecting only holes flowing in a channel and allowing electrons to pass through.
Here an npn-type transistor is explained. Alternatively, a pnp-type transistor can be applied.
As shown in FIG. 3, a plurality of partial quantum-wave interference layers Ik may be formed corresponding to each of a plurality of kinetic energy levels Ek. Each of the partial quantum-wave interference layers Ik has Tk periods of a pair of a first layer W and a second layer B whose respective thicknesses (DWk, DBk) are determined by Eqs. 3 and 4. The plurality of the partial quantum-wave interference layer Ik is arranged in series with respect to the number k of kinetic energy levels Ek. That is, the quantum-wave interference layer is formed by a serial connection of I1, I2, . . . , and Ij. As shown in FIG. 3, electrons with each of the kinetic energy levels Ek are reflected by the corresponding partial quantum-wave interference layers Ik. Accordingly, electrons belonging to each of the kinetic energy levels from E1 to Ej are reflected effectively. By designing the intervals between the kinetic energies to be short, thicknesses of the first layer W and the second layer B (DWk, DBk) in each of the partial quantum-wave interference layers Ik vary continuously with respect to the value k.
As shown in FIG. 4, a plurality of partial quantum-wave interference layers may be formed with an arbitrary period. Each of the partial quantum-wave interference layers, I1, I2, . . . is made of serial pairs of the first layer W and the second layer B with widths (DWk, DBk) determined by Eqs. 3 and 4. That is, the partial quantum-wave interference layer, e.g., I1, is constructed with serial layers of width (DW1, DB1), (DW2, DB2), . . . , (DWj, DBj), as shown. A plurality I1, I2, . . . of layers such as layer I1 are connected in series to form the total quantum-wave interference layer. Accordingly, electrons of the plurality of kinetic energy levels Ek are reflected by each pair of layers in each partial quantum-wave interference layers. By designing the intervals between kinetic energies to be short, thicknesses of the pair of the first layer W and the second layer B (DWk, DBk) in a certain partial quantum-wave interference layer varies continuously with respect to the value k.
The second and sixth aspects of the present invention are directed forming a xcex4 layer at the interface between. the first layer W and the second layer B. The xcex4 layer has an adequately thinner thickness than both of the first layer W and the second layer B and sharply varies an energy band. Reflectivity R of the interfaces determined by Eq. 7. By forming the xcex4 layer, the potential energy V of an energy band becomes larger and the value x of Eq. 7 becomes smaller. Accordingly, the reflectivity R becomes larger. Also, by sharply varying the band gap of the interfaces, the potential energy V of an energy band becomes larger and the value x of Eq. 7 becomes smaller. Without forming a xcex4 layer, a part of component of the first layer W and the second layer B mixes when the second layer B is laminated on the first layer W, and an energy band gap which varies sharply cannot be obtained. When a xcex4 layer is formed at each interfaces of the first and the second layers, even if a part of component of the first layer W and the second layer B mixes, an energy band gap varies sharply compared with the case without xcex4 layers.
Variations are shown in FIGS. 5A to 5C. The xcex4 layer may be formed on-both ends of the every first layer W as shown in FIGS. 5A to 5C. In FIG. 5A, the xcex4 layers are formed so that an energy level higher than that of the second layer B may be formed. In FIG. 5B, the xcex4 layers are formed so that a band having lower bottom than that of the first layer w may be formed. In FIG. 5C, the xcex4 layers are formed so that the energy level higher than that of the second layer B and the energy level lower than that of the first layer W may be formed. As an alternative to each of the variations shown in FIGS. 5A to 5C, the xcex4 layer can be formed on one end of the every first layer W.
Forming one xcex4 layer realizes large quantum-wave reflectivity at the interface between the first layer W and the second layer B and a plurality of the xcex4 layers realizes a larger reflectivity as a whole.
The seventh aspect of the present invention is directed to a quantum-wave interference layer that functions as a reflecting layer and selectively confines carriers in the channel in the front of the quantum-wave interference layer.
The eighth aspect of the present invention, or forming a thick second layer B0 at the side of an incident plane of the quantum-wave interference layer, and effectively prevents conduction by tunneling effects and reflects carriers.